"I have two Finnish dogs and one Norwegian cat."
Translation:Minulla on kaksi suomalaista koiraa ja yksi norjalainen kissa.
Yes, the plural form of "yksi" is "yhdet". It would refer to one set of something. Perhaps one of the most common examples is something along the lines of "otetaan vielä yhdet", which means "let's have another round of drinks". It's also used with plurale tantum nouns, i.e. nouns that are always plural, such as "furniture" (the Finnish equivalent "huonekalu" can be singular too). A Finnish example would be "häät", which means "wedding" (note that the Finnish word is plural even though the English translation is singular). An example sentence would be "siellä oli meneillään yhdet häät", meaning "there was a (certain) wedding going on there". "Kolmet" refers to three sets of something, such as "kolmet kengät", meaning "three pairs of shoes", and also three instances of plurale tantum nouns, such as "kolmet kasvot", meaning "three faces" (again note that the Finnish word is almost always plural even though its English equivalent commonly appears in singular form as well).
Wow. Thanks for that explanation! I'm learning a lot of new concepts in these comments, but I have a feeling this may be an especially difficult idea in Finnish. I get that first example: "let's have another one" (i.e. round of drinks), but is a wedding plural, conceptually, because there's more than one person involved? Can it take a singular form?